Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}x+2y &= 1 \\ -7x+6y &= -5\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = 7x-5$ Divide both sides by $6$ to isolate $y$ $y = {\dfrac{7}{6}x - \dfrac{5}{6}}$ Substitute this expression for $y$ in the first equation. $x+2({\dfrac{7}{6}x - \dfrac{5}{6}}) = 1$ $x + \dfrac{7}{3}x - \dfrac{5}{3} = 1$ Simplify by combining terms, then solve for $x$ $\dfrac{10}{3}x - \dfrac{5}{3} = 1$ $\dfrac{10}{3}x = \dfrac{8}{3}$ $x = \dfrac{4}{5}$ Substitute $\dfrac{4}{5}$ for $x$ back into the top equation. $ \dfrac{4}{5}+2y = 1$ $\dfrac{4}{5}+2y = 1$ $2y = \dfrac{1}{5}$ The solution is $\enspace x = \dfrac{4}{5}, \enspace y = \dfrac{1}{10}$.